Preheat oven to 425 degrees F. Combine all felafel ingredients except 1 tablespoon olive oil in the bowl of a food processor. Process for 10 seconds. Stop motor and scrape down sides of bowl, then pulse for another 10 seconds, until all ingredients are well incorporated but mixture is still slightly coarse and grainy. Form mixture into 16 felafel balls and brush with remaining tablespoon olive oil. Bake on a cookie sheet for 20 minutes, flip felafel balls and bake an additional 20 minutes, until felafel balls are crisp and browned.
Combine tahini, lemon juice and water and stir to incorporate, adding more water to achieve desired consistency. Reserve.
Toss together lettuce, tomatoes and cucumbers in a bowl. Warm pita breads for 2 minutes in oven. Fill each pita with 3/4 cup salad, 4 felafel balls and 1/4 cup tahini sauce.